An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points

An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points

Year:    2019

Author:    Yuan Chen, Songming Hou, Xu Zhang

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 5 : pp. 1005–1021

Abstract

Interface problems have wide applications in modern scientific research. Obtaining accurate numerical solutions of multi-domain problems involving triple junction conditions remains a significant challenge. In this paper, we develop an efficient finite element method based on non-body-fitting meshes for solving multi-domain elliptic interface problems. We follow the idea of immersed finite element by modifying local basis functions to accommodate interface conditions. We enrich the local finite element space by adding new basis functions for handling non-homogeneous flux jump. The numerical scheme is symmetric and positive definite. Numerical experiments are provided to demonstrate the features of our method.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0175

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 5 : pp. 1005–1021

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Immersed finite element interface problems triple junction multi-domain.

Author Details

Yuan Chen

Songming Hou

Xu Zhang

  1. A bilinear partially penalized immersed finite element method for elliptic interface problems with multi-domain and triple-junction points

    Chen, Yuan | Hou, Songming | Zhang, Xu

    Results in Applied Mathematics, Vol. 8 (2020), Iss. P.100100

    https://doi.org/10.1016/j.rinam.2020.100100 [Citations: 9]
  2. A class of nonconforming immersed finite element methods for Stokes interface problems

    Jones, Derrick | Zhang, Xu

    Journal of Computational and Applied Mathematics, Vol. 392 (2021), Iss. P.113493

    https://doi.org/10.1016/j.cam.2021.113493 [Citations: 16]